Related papers: An Elliptic Yangian-Invariant, `Leading Singularit…

We investigate the consequences of elliptic leading singularities for the unitarity-based representations of two-loop amplitudes in planar, maximally supersymmetric Yang-Mills theory. We show that diagonalizing with respect to these leading…

We take up the study of integrable structures behind non-planar contributions to scattering amplitudes in N=4 super Yang-Mills theory. Focusing on leading singularities, we derive the action of the Yangian generators on color-ordered…

In this article, we reconsider the formulation of Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory, and we investigate to what extent this symmetry lifts to the beta/gamma-deformation of the model. We first apply cohomology…

We present a multisymplectic formulation of the Yang--Mills equations. The connections are represented by normalized equivariant 1-forms on the total space of a principal bundle, with values in a Lie algebra. Within the multisymplectic…

In this letter we establish Yangian symmetry of planar N=4 super-Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover we propose an off-shell…

Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a remarkable symmetry structure. In addition to the superconformal symmetry of the Lagrangian of the theory, the planar amplitudes exhibit a dual superconformal symmetry.…

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in…

We study correlators of null, $n$-sided polygonal Wilson loops with a Lagrangian insertion in the planar limit of the ${\cal N}=4$ supersymmetric Yang-Mills theory. This finite observable is closely related to loop integrands of…

Planar N=4 supersymmetric Yang-Mills theory appears to be perturbatively integrable. This work reviews integrability in terms of a Yangian algebra and compares the application to the problems of anomalous dimensions and scattering…

We show that the Hamiltonian of (N=1;d=10) super Yang-Mills can be expressed as a quadratic form in a very similar manner to that of the (N=4;d=4) theory. We find a similar quadratic form structure for pure Yang-Mills theory but this…

In this article we establish the notion of classical Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory and for related planar gauge theories. After revisiting Yangian invariance for the equations of motion, we describe how…

Recently, new theoretical ideas have allowed the construction of lattice actions which are explicitly invariant under one or more supersymmetries. These theories are local and free of doublers and in the case of Yang-Mills theories also…

The spectrum of N=1 supersymmetric Yang-Mills theory, calculated on the lattice, is presented. The masses have been determined on three different lattice spacings and extrapolated towards vanishing gluino mass. We present the extrapolation…

The planar Yang-Mills theory in three spatial dimensions is examined in a particular representation which explicitly embodies factorization. The effective planar Yang-Mills theory Hamiltonian is constructed in this representation.

We calculate the general planar dual-conformally invariant double-pentagon and pentabox integrals in four dimensions. Concretely, we derive one-fold integral representations for these elliptic integrals over polylogarithms of weight three.…

In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with a paper "On maximally supersymmetric Yang-Mills theories" devoted to maximally…

We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations…

We apply novel techniques in planar superconformal Yang-Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with the first two local abelian Hamiltonians with…

We demonstrate that the planar real-$\beta$-deformed Super-Yang--Mills theory possesses an infinitely-dimensional Yangian symmetry algebra and thus is classically integrable. This is achieved by the introduction of the twisted coproduct…

It is proposed an integral formulation of classical Yang-Mills equations in the presence of sources, based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. The formulation leads…